What is Mathematics? Bulletin American Mathematical Society Vol. 18 (1912), pp. 386-387.
[841]. Every man is ready to join in the approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton’s Quaternions, and show us wherein it is superior to Newton’s Fluxions?—Hill, Thomas.
Imagination in Mathematics; North American Review, Vol. 85, p. 224.
[842]. The pursuit of mathematical science makes its votary appear singularly indifferent to the ordinary interests and cares of men. Seeking eternal truths, and finding his pleasures in the realities of form and number, he has little interest in the disputes and contentions of the passing hour. His views on social and political questions partake of the grandeur of his favorite contemplations, and, while careful to throw his mite of influence on the side of right and truth, he is content to abide the workings of those general laws by which he doubts not that the fluctuations of human history are as unerringly guided as are the perturbations of the planetary hosts.—Hill, Thomas.
Imagination in Mathematics; North American Review, Vol. 85, p. 227.
[843]. There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.—Hill, Thomas.
Imagination in Mathematics; North American Review, Vol. 85, p. 223.
[844]. To think the thinkable—that is the mathematician’s aim.—Keyser, C. J.
The Universe and Beyond; Hibbert Journal, Vol. 3 (1904-1905), p. 312.
[845]. Every common mechanic has something to say in his craft about good and evil, useful and useless, but these practical considerations never enter into the purview of the mathematician.—Aristippus the Cyrenaic.